Chapter 5,

Chapter 5, "Matrix Operations"

Equal Matrices

Two matrices are equal if

• Both matrices have equal dimensions.

• All corresponding entries are equal.

Adding Matrices

For two matrices of the same size , add the corresponding entries.

Subtracting Matrices

For two matrices of the same size, subtract the corresponding entries.

Scalar Multiplication

for any scalar value c and any size matrix A.

Multiplying Two 2x2 Matrices

Is the Product Defined?

For matrix multiplication AB, the number of columns in A must equal the number of rows in B.

Size of the Product

If AB is defined, the size of matrix AB is the number of rows in A by the number of columns in B.

Matrix Multiplication Is Not Commutative

AB BA

for any size matrices A and B.

Transpose for a 3x3 Matrix

Transpose

For any size matrix A, each entry a _mn moves to a _nm in A ^T .